That is literally the exact opposite of what Coase said.
Coase said that in a world without transaction costs it doesn't matter who the liability falls upon. When you turn to the real world, the fact that it matters greatly who the liability falls on shows just how important transaction costs are.
Coase was trying to get economist to stop ignoring transaction costs and pretending that the type of bargaining in your comment will solve all our problems.
Here's Coase himself:
The world of zero transaction costs has often been
described as a Coasian world. Nothing could be further
from the truth. It is the world of modern economic
theory, one which I was hoping to persuade economists
to leave
Coase said that in a world without transaction costs it doesn't matter who the liability falls upon. When you turn to the real world, the fact that it matters greatly who the liability falls on shows just how important transaction costs are.
Coase was trying to get economist to stop ignoring transaction costs and pretending that the type of bargaining in your comment will solve all our problems.
Here's Coase himself:
Here, read this (pdf). It explains your misunderstanding (shared by many others) in great detail: http://www.deirdremccloskey.com/docs/pdf/Article_306.pdf